Problem: Simplify the following expression: $y = \dfrac{-9k^2 + 90k - 216}{k - 6} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ y =\dfrac{-9(k^2 - 10k + 24)}{k - 6} $ Then we factor the remaining polynomial: $k^2 {-10}k + {24} $ ${-6} {-4} = {-10}$ ${-6} \times {-4} = {24}$ $ (k {-6}) (k {-4}) $ This gives us a factored expression: $\dfrac{-9(k {-6}) (k {-4})}{k - 6}$ We can divide the numerator and denominator by $(k + 6)$ on condition that $k \neq 6$ Therefore $y = -9(k - 4); k \neq 6$